Подсказки 20.3+ умеют возвращать адреса латиницей, если в запросе указать параметр language = en:

{
    "query": "Москва Турчанинов 2 кв 25",
    "language": "EN"
}

Ответ:

{
    "suggestions": [
        {
            "value": "Russia, Moscow city, pereulok Turchaninov, dom 2, kvartira 25",
            "unrestricted_value": "119034, Russia, Moscow city, raion Hamovniki, pereulok Turchaninov, dom 2, kvartira 25",
            "data": {
                "postal_code": "119034",
                "country": "Russia",
                "country_iso_code": "RU",
                "federal_district": "Centralnyi",
                "region_fias_id": "0c5b2444-70a0-4932-980c-b4dc0d3f02b5",
                "region_kladr_id": "7700000000000",
                "region_iso_code": "RU-MOW",
                "region_with_type": "Moscow city",
                "region_type": "city",
                "region_type_full": "city",
                "region": "Moscow",
                "area_fias_id": null,
                "area_kladr_id": null,
                "area_with_type": null,
                "area_type": null,
                "area_type_full": null,
                "area": null,
                "city_fias_id": "0c5b2444-70a0-4932-980c-b4dc0d3f02b5",
                "city_kladr_id": "7700000000000",
                "city_with_type": "Moscow city",
                "city_type": "city",
                "city_type_full": "city",
                "city": "Moscow",
                "city_area": "Centralnyi",
                "city_district_fias_id": null,
                "city_district_kladr_id": null,
                "city_district_with_type": "raion Hamovniki",
                "city_district_type": "raion",
                "city_district_type_full": "raion",
                "city_district": "Hamovniki",
                "settlement_fias_id": null,
                "settlement_kladr_id": null,
                "settlement_with_type": null,
                "settlement_type": null,
                "settlement_type_full": null,
                "settlement": null,
                "street_fias_id": "0f7981e6-65c6-4513-b771-f5db3bfafe60",
                "street_kladr_id": "77000000000714800",
                "street_with_type": "pereulok Turchaninov",
                "street_type": "pereulok",
                "street_type_full": "pereulok",
                "street": "Turchaninov",
                "house_fias_id": "980b6072-c88a-4ca0-993e-2496632b6a31",
                "house_kladr_id": "7700000000071480001",
                "house_type": "dom",
                "house_type_full": "dom",
                "house": "2",
                "block_type": null,
                "block_type_full": null,
                "block": null,
                "flat_type": "kvartira",
                "flat_type_full": "kvartira",
                "flat": "25",
                "flat_area": null,
                "square_meter_price": "1159541",
                "flat_price": null,
                "postal_box": null,
                "fias_id": "980b6072-c88a-4ca0-993e-2496632b6a31",
                "fias_code": "77000000000000071480001",
                "fias_level": "8",
                "fias_actuality_state": "0",
                "kladr_id": "7700000000071480001",
                "geoname_id": null,
                "capital_marker": "0",
                "okato": "45286590000",
                "oktmo": "45383000",
                "tax_office": "7704",
                "tax_office_legal": "7704",
                "timezone": "UTC+3",
                "geo_lat": "55.7366228",
                "geo_lon": "37.5983198",
                "beltway_hit": "IN_MKAD",
                "beltway_distance": null,
                "metro": [
                    {
                        "name": "Park kultury",
                        "line": "Sokolnicheskaya",
                        "distance": 0.2
                    },
                    {
                        "name": "Park kultury",
                        "line": "Kolcevaya",
                        "distance": 0.4
                    },
                    {
                        "name": "Kropotkinskaya",
                        "line": "Sokolnicheskaya",
                        "distance": 1.0
                    }
                ],
                "qc_geo": "0",
                "qc_complete": null,
                "qc_house": null,
                "history_values": null,
                "unparsed_parts": null,
                "source": null,
                "qc": null
            }
        }
    ]
}